Statistics - Inverse Gamma Distribution



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Inverse Gamma Distribution is a reciprocal of gamma probability density function with positive shape parameters $ {\alpha, \beta } $ and location parameter $ { \mu } $. $ {\alpha } $ controls the height. Higher the $ {\alpha } $, taller is the probability density function (PDF). $ {\beta } $ controls the speed. It is defined by following formula.

Formula

${ f(x) = \frac{x^{-(\alpha+1)}e^{\frac{-1}{\beta x}}}{ \Gamma(\alpha) \beta^\alpha} \\[7pt] \, where x \gt 0 }$

Where −

  • ${\alpha}$ = positive shape parameter.

  • ${\beta}$ = positive shape parameter.

  • ${x}$ = random variable.

Following diagram shows the probability density function with different parameter combinations.

Inverse Gamma Distribution

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